I came across this question, and found the same meaning in the dictionary for both options
(a-危ない) or (b-危うい) ですから 下がってください
however the answer booklet says it is (a-危ない), what is the difference?
They have the same meaning of "dangerous", but 危うい is used more in the written language (文語), whereas 危ない is used more in the spoken language (口語).
Here's a Chiebukuro question asking about this.
大辞林 has a note in the entry for 危ない
(Warning: possibly inaccurate translation ahead). Basically it says that 危ない has replaced 危うい in modern times. Nowadays, the usage of 危うい is literary-like, and expresses the urgency/imminence of a worst case scenario like death or decimation. In contrast with that, 危ない expresses that something bad is going to happen, regardless of whether it involves bodily harm (threat to life) or not.
Additionally, in 語源's entry on 危ない, it mentions that
The 元々 seems to suggest that it is not the case now though, hmm...
危ない is "dangerous" while 危うい is "vulnerable" or "not reliable".
In theory, both are correct because the meaning is the same. 危うい and 危ない have the same meaning of "Dangerous".
But you should have to know the context in the case of 「危ないですから、下がってください」. This is a typical audio message that is heard in the station when the train arrives. So, in that case only 危ない is the correct word, because 危うい is only used in the written language.
And yes, as always the Nihongo Sou Matome book (the source of that question) doesn't explain anything about this.